Real numbers. Exponentials and logarithms
Formalism of vectors.
Trigonometry.
Concept of limit; differential and integral calculus.
Analytic study of functions.
G. Anichini, G. Conti, R. Paoletti, Algebra lineare e geometria analitica. Ed Pearson
G. Anichini, G. Conti, M. Spadini, Analisi Matematica 1. Ed Pearson.
G. Anichini, A. Carbone, P. Chiarelli, G. Conti, Precorso di Matematica, Ed. Pearson
Learning Objectives
Knowledge and comprehension of the mathematical formalism relevant to the characterizing courses of the cursus studiorum.
Ability on applying the knowledge and comprehension on mathematica tools to describe and solve problems.
Autonomy of judgement on critical evaluation of a mathematical text, on selecting a proper path to the solution of problems, and on the verification of achieved results.
Comunicative skills on translating data described in current Italian language into mathematical formalism and viceversa.
Ability on learning concepts of modern mathematics such as differential and integral calculus.
Prerequisites
Arithmetics of real numbers.
Notions of synthetic geometry.
Notions of literal calculus.
Teaching Methods
Frontal lessons
Further information
Every student in need of specific auxiliary support can request it by email to the professor.
Type of Assessment
Mandatory written and oral exam.d.
Course program
Real numbers and algebraic laws: .
Euclidean distance: Cartesian coordinates on a straight line, on a plane, on the space; Pythagoras theorem and calculus of distance.
Angles: not oriented and oriented; sine, cosine, tangent, cotangent, and their inverse of the measure of an angle; polar coordinates.
Straight lines on a plane: how to determine the cartesian equation. Geometric interpretation and resolution of linear system of equations.
Vectors, scalar product, sum of vectors, product of a scalar times a vector, canonical writing of a vector; orthogonal projection of a vector; cross product.
Equations and inequalities: techniques to solve them; determination of the sign of expressions.
Asymptotes and continuity: notion of limit; operations with limits.
Differential calculus: de l'Hospital theorem; monotonicity and sign of first derivative; second derivative and convexity; theorems on differentiable functions; critical points.
Integral calculus: definite, indefinite, improper integral and techniques of computation.